David Cameron has axed standard assessments used to gauge how policies affect different social groups as part of a drive to get rid of the "bureaucratic rubbish" that gets in the way of British business.

Cameron also vowed to slash three-month consultation periods on future government policy proposals, signalling that the public may not get a say at all on some proposals, with the final decision left to individual ministers. Other measures include reducing the time limit for bringing judicial reviews, hiking up the legal charge involved, and halving the number of possible appeals.

The prime minister outlined plans to axe equality impact assessments at the CBI conference, saying new government measures needed to be "tough, radical and fast" to help British business compete in the global race. He said "faster government" was one of the key steps Britain needs to take to thrive – "in this global race you are quick or you're dead", he said.

Cameron said that while "massive steps" had already been taken to make government leaner and faster, further measures were needed because government "can still be far too slow at getting stuff done.

"Consultations, impact assessments, audits, reviews, stakeholder management, securing professional buy-in, complying with EU procurement rules, assessing sector feedback … this is not how we became one of the most powerful, prosperous nations on Earth. It's not how you get things done. As someone once said, if Christopher Columbus had an advisory committee he would probably still be stuck in the dock. So I am determined to change this."

Cameron said the Equality Act was "not a bad piece of legislation", it was just the way it had been interpreted – with equality impact assessments on every policy, "way beyond" what was required, he said.

Speaking in central London, Cameron said it could be left instead to "smart people in Whitehall" to consider equality issues while making policies.

"Let me be very clear. I care about making sure that government policy never marginalises or discriminates," he said. "I care about making sure we treat people equally. But let's have the courage to say it – caring about these things does not have to mean churning out reams of bureaucratic nonsense. We have smart people in Whitehall who consider equalities issues while they're making the policy. We don't need all this extra tick-box stuff. So I can tell you today, we are calling time on equality impact assessments. You no longer have to do them if these issues have been properly considered."

The prime minister also announced measures to clamp down on the "massive growth industry" of judicial reviews, which he said had almost tripled over a decade. He claimed many of them were "completely pointless" and had delayed major projects.

"Of course some are well-founded, as we saw with the west coast main line decision," he said. "But let's face it: so many are completely pointless. Last year, an application was around five times more likely to be refused than granted. We urgently needed to get a grip on this."

He announced a reduction on the time limit for bringing cases, charging more for reviews "so people think twice about time-wasting", and halving the number of appeals for "hopeless cases" from four to two.

He also vowed to end the three-month consultation period "on everything and I mean everything, no matter how big or small" that the coalition had inherited.

"So we are saying to ministers: here's a revolutionary idea – you decide how long a consultation period this actually needs. If you can get it done properly in a fortnight, great; indeed, the Department for Education has already had a consultation done and dusted in two weeks. And we are going further, saying, if there is no need for a consultation, then don't have one."

Cameron told the conference that the country was mired "in the economic equivalent of war" and that the spirit evoked in the 1940s needed to be applied to the current economic challenge. "We need to forget about crossing every 't' and dotting every 'i' and we need to throw everything we've got at winning in this global race."

He added: "You know what the global race means because you're living it. And I'm here today to tell you this government gets it. We get that the world is breathing down our neck. And we get what British business needs. You need us to deal with our deficit. To cut business taxes so we can compete.

"To have a proper industrial strategy to get behind the growth engines of the future. To reform education so we turn out the brightest graduates and school-leavers. To reform welfare so it pays to work. These are the key steps to Britain thriving in this global race. But it's not just about policies, it's about attitude."